After engineering an ample number of opportunities open for you it depends on you, what you want to make yourself, you can go for higher studies according to your interest either M. Tech or MBA.

There are various competitive exam held on the basis of graduation degree.
Ample of fields are open to you after engineering.

No this is not true.
You can work in other sectors too.
Like software industry, financial sector, management jobs, banking, teaching, civil services and what not.